Even if means whether or not and has to do with the conditions that may apply. Even if is used as a conjunction.(even alone cannot act as a conjunction).
Even though means despite the fact that and is a more emphatic version of though and although.
- Even though he lost his job as Math Teacher, he continued to teach in the college. - describes a real situation where the Math teacher lost his job, but continues to teach in the college. When we attach even to though in this way, we are in effect saying: you may find this surprising but..
- Even if he loses his job as Math Teacher, I think he'll continue to teach in the college. - describes an unreal situation where we could substitute 'just supposing' for even if and say: just supposing he loses his job as Math teacher, he would still continue teaching in the college.
